Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 15 mL. A sample of 16 bottles has a mean of 68.25 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 68.25 mLσ = 15 mLn = 16

z =

2.Easy

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 5 mL. A sample of 49 bottles has a mean of 76.71 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 76.71 mLσ = 5 mLn = 49

z =

3.Medium

The mean of a population is claimed to be 500; the population standard deviation is known to be 30. A random sample of 100 observations has a mean of 504.26. Test H₀: μ = 500 against H₁: μ > 500. Find the p-value p.

μ₀ = 500σ = 30n = 100x̄ = 504.26H₁: μ > μ₀

p =

4.Medium

A sample of 64 students has a mean score of 100.6 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 100.6s = 4n = 64

t =

5.Hard

A sample of 49 measurements has mean 119.3. The population standard deviation is 4. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 119.3σ = 4n = 4999%

L =

6.Hard

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 2.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 2.595%

n =

Answer key

1. z = −1.8
2. z = 2.394
3. p = 0.0778
4. t = 1.2
5. L = 117.8
6. n = 139

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